David's distance

Geometry Level 4

Let \(ABCD\) be a rectangle such that \(AB=5\) and \(BC=12\). There exist two distinct points \(X_1\) and \(X_2\) on \(BC\) such that \(\angle AX_1D=\angle AX_2D=90^\circ\). Suppose that \(d\) is the distance from \(X_1\) to \(X_2\). What is \(d^2\)?

This problem is posed by David A.

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